TSTP Solution File: BOO010-4 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : BOO010-4 : TPTP v8.1.0. Released v1.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n021.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Thu Jul 14 23:49:24 EDT 2022
% Result : Unsatisfiable 0.19s 0.42s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 9
% Syntax : Number of clauses : 26 ( 26 unt; 0 nHn; 26 RR)
% Number of literals : 26 ( 0 equ; 2 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 7 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
~ equal(add(a,multiply(a,b)),a),
file('BOO010-4.p',unknown),
[] ).
cnf(2,axiom,
equal(add(u,v),add(v,u)),
file('BOO010-4.p',unknown),
[] ).
cnf(3,axiom,
equal(multiply(u,v),multiply(v,u)),
file('BOO010-4.p',unknown),
[] ).
cnf(4,axiom,
equal(multiply(add(u,v),add(u,w)),add(u,multiply(v,w))),
file('BOO010-4.p',unknown),
[] ).
cnf(5,axiom,
equal(add(multiply(u,v),multiply(u,w)),multiply(u,add(v,w))),
file('BOO010-4.p',unknown),
[] ).
cnf(6,axiom,
equal(add(u,additive_identity),u),
file('BOO010-4.p',unknown),
[] ).
cnf(7,axiom,
equal(multiply(u,multiplicative_identity),u),
file('BOO010-4.p',unknown),
[] ).
cnf(8,axiom,
equal(add(u,inverse(u)),multiplicative_identity),
file('BOO010-4.p',unknown),
[] ).
cnf(9,axiom,
equal(multiply(u,inverse(u)),additive_identity),
file('BOO010-4.p',unknown),
[] ).
cnf(28,plain,
equal(add(additive_identity,u),u),
inference(spr,[status(thm),theory(equality)],[2,6]),
[iquote('0:SpR:2.0,6.0')] ).
cnf(45,plain,
equal(add(multiply(u,v),u),multiply(u,add(v,multiplicative_identity))),
inference(spr,[status(thm),theory(equality)],[7,5]),
[iquote('0:SpR:7.0,5.0')] ).
cnf(46,plain,
equal(multiply(u,add(v,inverse(u))),add(multiply(u,v),additive_identity)),
inference(spr,[status(thm),theory(equality)],[9,5]),
[iquote('0:SpR:9.0,5.0')] ).
cnf(55,plain,
equal(add(u,multiply(u,v)),multiply(u,add(v,multiplicative_identity))),
inference(rew,[status(thm),theory(equality)],[2,45]),
[iquote('0:Rew:2.0,45.0')] ).
cnf(56,plain,
~ equal(multiply(a,add(b,multiplicative_identity)),a),
inference(rew,[status(thm),theory(equality)],[55,1]),
[iquote('0:Rew:55.0,1.0')] ).
cnf(60,plain,
equal(multiply(u,add(v,inverse(u))),multiply(u,v)),
inference(rew,[status(thm),theory(equality)],[28,46,2]),
[iquote('0:Rew:28.0,46.0,2.0,46.0')] ).
cnf(70,plain,
equal(multiply(u,multiplicative_identity),multiply(u,u)),
inference(spr,[status(thm),theory(equality)],[8,60]),
[iquote('0:SpR:8.0,60.0')] ).
cnf(73,plain,
equal(multiply(u,inverse(u)),multiply(u,additive_identity)),
inference(spr,[status(thm),theory(equality)],[28,60]),
[iquote('0:SpR:28.0,60.0')] ).
cnf(74,plain,
equal(multiply(u,u),u),
inference(rew,[status(thm),theory(equality)],[7,70]),
[iquote('0:Rew:7.0,70.0')] ).
cnf(76,plain,
equal(multiply(u,additive_identity),additive_identity),
inference(rew,[status(thm),theory(equality)],[9,73]),
[iquote('0:Rew:9.0,73.0')] ).
cnf(86,plain,
equal(multiply(add(u,v),u),add(u,multiply(v,additive_identity))),
inference(spr,[status(thm),theory(equality)],[6,4]),
[iquote('0:SpR:6.0,4.0')] ).
cnf(98,plain,
equal(multiply(u,add(u,v)),add(u,multiply(v,additive_identity))),
inference(rew,[status(thm),theory(equality)],[3,86]),
[iquote('0:Rew:3.0,86.0')] ).
cnf(99,plain,
equal(multiply(u,add(u,v)),add(u,additive_identity)),
inference(rew,[status(thm),theory(equality)],[76,98]),
[iquote('0:Rew:76.0,98.0')] ).
cnf(100,plain,
equal(multiply(u,add(u,v)),u),
inference(rew,[status(thm),theory(equality)],[6,99]),
[iquote('0:Rew:6.0,99.0')] ).
cnf(133,plain,
equal(add(u,multiply(u,v)),multiply(u,add(u,v))),
inference(spr,[status(thm),theory(equality)],[74,5]),
[iquote('0:SpR:74.0,5.0')] ).
cnf(142,plain,
equal(multiply(u,add(v,multiplicative_identity)),u),
inference(rew,[status(thm),theory(equality)],[55,133,100]),
[iquote('0:Rew:55.0,133.0,100.0,133.0')] ).
cnf(143,plain,
$false,
inference(unc,[status(thm)],[142,56]),
[iquote('0:UnC:142.0,56.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : BOO010-4 : TPTP v8.1.0. Released v1.1.0.
% 0.03/0.12 % Command : run_spass %d %s
% 0.11/0.33 % Computer : n021.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 600
% 0.11/0.33 % DateTime : Thu Jun 2 00:15:01 EDT 2022
% 0.11/0.33 % CPUTime :
% 0.19/0.42
% 0.19/0.42 SPASS V 3.9
% 0.19/0.42 SPASS beiseite: Proof found.
% 0.19/0.42 % SZS status Theorem
% 0.19/0.42 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.42 SPASS derived 102 clauses, backtracked 0 clauses, performed 0 splits and kept 42 clauses.
% 0.19/0.42 SPASS allocated 63230 KBytes.
% 0.19/0.42 SPASS spent 0:00:00.07 on the problem.
% 0.19/0.42 0:00:00.04 for the input.
% 0.19/0.42 0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.42 0:00:00.00 for inferences.
% 0.19/0.42 0:00:00.00 for the backtracking.
% 0.19/0.42 0:00:00.01 for the reduction.
% 0.19/0.42
% 0.19/0.42
% 0.19/0.42 Here is a proof with depth 3, length 26 :
% 0.19/0.42 % SZS output start Refutation
% See solution above
% 0.19/0.42 Formulae used in the proof : prove_a_plus_ab_is_a commutativity_of_add commutativity_of_multiply distributivity1 distributivity2 additive_id1 multiplicative_id1 additive_inverse1 multiplicative_inverse1
% 0.19/0.42
%------------------------------------------------------------------------------